This... is a tough question for a couple of different reasons.

Firstly - in some situations, sometimes even today men cry and it is 'allowed' without penalty to masculinity - indeed, sometimes it is seen with approval. For example most people wouldn't think it strange if a man started to cry at the death of his child, as long as it was silent and his facial expression was still. The performance of masculinity is being undertaken in a way that expresses and simultaneously excuses the grief.

In terms of my own time period and cultural focus, which is early 20th century western military cultures; during periods of physical or otherwise crippling pain, tears can be an accepted sign of the truth of that pain - ie there is a physical effect on his wounded body that is outside of his control and his tears are an 'involuntary' symbol of that. Masculinity is then performed through sound - ie silence - and facial expression. (That men stayed silent through their obvious pain is often remarked upon with surprise in First World War hospital wards by female nurses' dairies).

But aside from that, people don't just cry from grief or pain - men might also cry for joy. A grandfather crying at the birth of a new grandchild would be seen with approval in 1914, for instance. To be honest I can't imagine the same situation would be seen with anything other than approval today.

So we've got that context.

Then it depends on what culture we're talking about. Jesus wept often in the bible, and it is noted more as a sign of his true emotion than anything to do with his masculinity. In Bali during the 1960s, for instance, it was not done for anyone to cry - it was not linked to masculinity, but to humanity. In old Norse sagas such as Beowulf, men wept freely over many things - Beowulf's death leaves his liege-men devastated, and they weep. It is a testament to the truth of emotion.

Crying is a culturally constructed thing, and so is masculinity - like any culturally constructed thing, attitudes towards it change over time, and get negotiated with specific contexts - or are constructed entirely differently from place to place. So your question is arguably impossible to answer in broad terms, because it is both highly specific, while also being completely different. Does that make sense?

EDIT: for clarity.

No. In many cultures, there are certain "manly" ways to cry. This is not to say that all crying has been acceptable, or that crying wasn't still in some way "gendered" with different contexts where men and women were expected or allowed to cry. I hope the mods will forgive me for using recent examples from the last twenty years, but they're the first that come to mind. However, they are unambiguously indicative of a broader norms within in Islam that go back centuries.

The political scientist Thomas Hegghammer has a good article called "Why Terrorists Weep: The Socio-Cultural Practices of Jihadi Militants". It was an invited lecture, not a peer reviewed article, but it's very very interesting (especially if you know something of his trajectory as a scholar and political science as a discipline: such an interest in culture is historically rather rare in political science). You can read the lecture on Academia.edu or on his website.

As he puts it, the lecture has "a fancy title, but it is basically about what jihadis do in their spare time". He continues:

My starting point is the truism that military life is about much more than fighting. Look inside any militant group – or conventional army for that matter – and you will see lots of artistic products and social practices that serve no obvious military purpose. Think of the cadence calls of the U.S. Marines, the songs of leftist revolutionaries, or the tattoos of neo-nazis. Look inside jihadi groups and you’ll see bearded men with kalashnikovs reciting poetry, discussing dreams, and weeping on a regular basis.

It took me a long time to even notice these things. I’ve studied jihadi groups for almost fifteen years, and for the first ten, I was addressing standard questions, like, how did group A evolve, what has ideologue B written, who joins movement C, etc. The thing is, when you study one type of group for a while, you take certain things for granted. I knew that these groups were weeping and reading poetry, but it didn’t really register - it was background noise to me, stuff I needed to shove aside to get to the hard information about people and events.

Then it occurred to me one day that these practices are not obvious at all; in fact, they are really quite strange. For one, there is the incongruence of hard men doing soft things. It is curious, for example, that Abu Mus’ab al-Zarqawi should be known simultaneously as “al-dhabbah” (the slaughterer) and “al-baki” (he who weeps a lot).

The rest of the lecture mainly sketches out a research program for Jihadi culture (if anyone is interest in Jihadi poetry in particular, in addition to the many works Hegghammer mentions, the eminent Middle Easternist Bernard Haykel and the literary critic Robyn Creswell had an interesting article about ISIS poetry in the New Yorker last summer), but toward the end he returns to poetry and weeping and its place within larger Arab-Islamic context.

As for the weeping, it seemed to occur mostly in devotional settings (especially during Qur’an recitation), but also in speeches and recruitment appeals, and occasionally for other, more ordinary reasons (after losing a friend, for example). In the jihadi underground, weeping is clearly socially appreciated, as a sign of devotion to God and to the cause. This notion is not specific to jihadis, but part of Islamic tradition. The medieval theologian al-Ghazali, for example, wrote extensively on the benefits of weeping.

There is some geographical variation, especially between jihadis in the West, who have incorporated many elements of Western street culture, and militants in the “East”. It also seems that poetry, for example, is appreciated more by jihadis from the Arabian Peninsula than from other places. But many cultural elements, like anashid, weeping, dream interpretation, were “everywhere”, which suggests jihadi culture has a core that is truly global.

/u/Fibonacci35813, I know you do psychology, so I thought you might interested in his argument that this sort of thick culture for jihadis and other similar militant groups functions as "a resource for costly signs of trustworthiness", as in very standard game theoretical accounts of signaling, and additionally functions as "emotional persuasion tools that reinforce the cognitive persuasion work done by doctrine".

But more importantly, this kind of weeping from passion, from deeply held feelings, is clearly not taboo in for men in these particularly circumstance, most of which are related directly or indirectly to deeply held religious feelings. If you want to see what this looks like, you can see it in the Vice News "Inside the Islamic State" documentary (for mobile users, the actual crying starts shortly after 12:15, but the whole scene with the preacher who cries starts around 11:05).

People are most interested in jihadi tears, but these tears a much broader cultural phenomenon in the Muslim World, even outside the Arab World. The much, much more moderate Islamist Turkish President, R. Tayip Erdoğan, similarly emphasizes that he literally cries for Palestinians. Here's a short video of him crying while listening to a poem, as another example (here's an editorial about that moment, though I think it's clear that the author is a secular Turk and so arguably does not understand how Erdoğan's more religious supporters see his tears). It's hard to describe exactly, but when I see women crying on Turkish television (especially the Turkish news), they don't cry like that. There's just a different repertoire of gestures, I feel, which marks Erdoğan's tears as acceptably separate from the very emotive wailing of, say, mothers who lost their sons. Just as in /u/CrossyNZ's post about acceptable masculine crying in the 20th century West, Erdoğan's crying was silent and his facial expression mostly still.

In all these cases, crying is not taboo, but rather demonstrates a pious, and suitably masculine, authenticity.

Depends on culture as well. In Heian-era Japan, it was not only acceptable but expected for men to weep at moments of high emotion, so much so that there was a literary formula for it. The Heike Monogatari, or "Tale of the Heike", a chronicle of the Gempei wars compiled from an old oral tradition, is replete with the phrase, "He wet his sleeve with his tears". The translation is by Helen Craig McCullough, and is quite brilliant - she even manages to capture some of the poetry, which is hideously difficult when translating from East Asian languages.